Ubuntu Manpage: fitcircle - find mean position and pole of best-fit great [or small] circle to points on a sphere.

Provided by: gmt-common_5.2.1+dfsg-3build1_all

NAME

       fitcircle - find mean position and pole of best-fit great [or small] circle to points on a sphere.

SYNOPSIS

       fitcircle  [ table ] norm [ flags ] [ [lat] ] [ [level] ] [ -bi<binary> ] [ -di<nodata> ] [ -f<flags> ] [
       -g<gaps> ] [ -h<headers> ] [ -i<flags> ] [ -o<flags> ] [ -:[i|o] ]

       Note: No space is allowed between the option flag and the associated arguments.

DESCRIPTION

fitcircle reads lon,lat [or lat,lon] values from the first two columns on standard input [or table].
These are converted to Cartesian three-vectors on the unit sphere. Then two locations are found: the mean
of the input positions, and the pole to the great circle which best fits the input positions. The user
may choose one or both of two possible solutions to this problem. The first is called -L1 and the second
is called -L2. When the data are closely grouped along a great circle both solutions are similar. If the
data have large dispersion, the pole to the great circle will be less well determined than the mean.
Compare both solutions as a qualitative check.

The -L1 solution is so called because it approximates the minimization of the sum of absolute values of
cosines of angular distances. This solution finds the mean position as the Fisher average of the data,
and the pole position as the Fisher average of the cross-products between the mean and the data.
Averaging cross-products gives weight to points in proportion to their distance from the mean, analogous
to the "leverage" of distant points in linear regression in the plane.

The -L2 solution is so called because it approximates the minimization of the sum of squares of cosines
of angular distances. It creates a 3 by 3 matrix of sums of squares of components of the data vectors.
The eigenvectors of this matrix give the mean and pole locations. This method may be more subject to
roundoff errors when there are thousands of data. The pole is given by the eigenvector corresponding to
the smallest eigenvalue; it is the least-well represented factor in the data and is not easily estimated
by either method.

REQUIRED ARGUMENTS

       -Lnorm Specify the desired norm as 1 or 2, or use -L or -L3 to see both solutions.

OPTIONAL ARGUMENTS

       table  One or more ASCII [or binary, see -bi] files containing lon,lat [or lat,lon; see  -:[i|o]]  values
              in the first 2 columns. If no file is specified, fitcircle will read from standard input.

       -Ff|m|n|s|c
              Normally,  fitcircle  will  write  its  results  in  the  form  of  a text report, with the values
              intermingled with report sentences.  Use -F to only return data coordinates, and append  flags  to
              specify  which  coordinates  you  would  like. You can choose from f (Flat Earth mean location), m
              (mean location), n (north pole of great circle), s (south pole of great circle), and c ** (pole of
              small circle and its colatitude, which requires **-S).

       -S[lat]
              Attempt to fit a small circle instead of a great circle. The pole will be constrained  to  lie  on
              the  great  circle  connecting  the pole of the best-fit great circle and the mean location of the
              data.  Optionally append the desired fixed latitude of the small circle  [Default  will  determine
              the latitude].

       -V[level] (more ...)
              Select verbosity level [c].

       -bi[ncols][t] (more ...)
              Select native binary input. [Default is 2 input columns].

       -dinodata (more ...)
              Replace input columns that equal nodata with NaN.

       -f[i|o]colinfo (more ...)
              Specify data types of input and/or output columns.

       -g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more ...)
              Determine data gaps and line breaks.

       -h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
              Skip or produce header record(s).

       -icols[l][sscale][ooffset][,...] (more ...)
              Select input columns (0 is first column).

       -ocols[,...] (more ...)
              Select output columns (0 is first column).

       -:[i|o] (more ...)
              Swap 1st and 2nd column on input and/or output.

       -^ or just -
              Print a short message about the syntax of the command, then exits (NOTE: on Windows use just -).

       -+ or just +
              Print  an  extensive usage (help) message, including the explanation of any module-specific option
              (but not the GMT common options), then exits.

       -? or no arguments
              Print a complete usage (help) message, including the explanation of options, then exits.

       --version
              Print GMT version and exit.

       --show-datadir
              Print full path to GMT share directory and exit.

ASCII FORMAT PRECISION

       The ASCII output formats of numerical data are controlled by parameters in your gmt.conf file.  Longitude
       and  latitude  are formatted according to FORMAT_GEO_OUT, whereas other values are formatted according to
       FORMAT_FLOAT_OUT. Be aware that the format in effect can lead to loss of precision in the  output,  which
       can  lead  to  various  problems downstream. If you find the output is not written with enough precision,
       consider  switching  to  binary  output  (-bo  if  available)  or  specify  more   decimals   using   the
       FORMAT_FLOAT_OUT setting.

EXAMPLES

       Suppose  you  have  lon,lat,grav data along a twisty ship track in the file ship.xyg. You want to project
       this data onto a great circle and resample it in distance, in order to filter it or check  its  spectrum.
       Do the following:

              gmt fitcircle ship.xyg -L2
              gmt project ship.xyg -Cox/oy -Tpx/py -S -Fpz | sample1d -S-100 -I1 > output.pg

       Here,  ox/oy  is  the  lon/lat of the mean from fitcircle, and px/py is the lon/lat of the pole. The file
       output.pg has distance, gravity data sampled every 1 km along the great circle which best fits ship.xyg

       If you have lon, lat points in the file data.txt and wish to return the northern hemisphere great  circle
       pole location using the L2 norm, try

              gmt fitcircle data.txt -L2 -Fn > pole.txt

COPYRIGHT

       2015, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe

5.2.1                                           January 28, 2016                                 FITCIRCLE(1gmt)